Equations for two-phase flow are used to analyze the one-dimensional sedimentation of solid particles in a stationary container of liquid. A derivation of the equations of motion is presented which is based upon Hamilton’s extended variational principle. The resulting equations contain diffusivity terms, which are linear in the gradient of the particle concentration. It is shown that the solution of the equations for steady sedimentation is stable under small perturbations. Finally, finite-difference solutions of the equations are compared to the data of Whelan, Huang, and Copley for blood sedimentation.

An extension of the effective stiffness theory developed for elastic laminates by Sun, Achenbach, and Herrmann [1] is presented in a form suitable for the solution of dynamical processes in composite materials including determination of stresses. A derivation of displacement and stress interface boundary conditions suitable for higher-order theories is presented. The theory is illustrated with dispersion and mode shape results for two examples of steady-state wave propagation.

For a simplified model of a laminated medium consisting of alternating layers of elastic and viscoelastic materials, the dispersion and attenuation characteristics for “plane,” longitudinal waves propagating in the direction of the layering are obtained. The dispersion and attenuation curves depend on a structure parameter involving the thickness of the layers and can deviate significantly from corresponding results for a continuum “effective-modulus” model. Curves are presented for a specific case with representative material parameters showing the effect of structure and of variations in the parameters of the composite.

A continuum theory, for a heat-conducting, porous elastic solid saturated by a mixture of heat-conducting, viscous compressible fluids, is developed using the continuum theory of mixtures. Gradients of the fluid densities and the second deformation gradient of the solid constituent are included among the independent constitutive variables as proposed by Mu¨ller [17]. The Clausius-Duhem entropy inequality and the principle of material indifference are used to obtain rational constitutive relations for the medium. Linear constitutive equations are presented, and a theory equivalent to a generalization of the Biot equations is obtained.

A theory of composite materials is proposed which is based on the continuum theory of mixtures. The constituents of a composite are modeled as superimposed continua which undergo individual deformations. Effects of structure on dynamical processes in composite materials are then simulated by specifying the coupling between the individual constituent motions. A novel feature of this model is the inclusion of diffusion with relative displacement coupling for perfectly bonded composites. A simple one-dimensional form of such a theory is presented, and, when compared with classical solutions for longitudinal wave propagation in laminated materials, predicts some aspects of the dynamical behavior extremely well.